It's worth noting that Equal Earth isn't an equidistant projection. The upper bound on distance distortion is an order of magnitude less than Mercator's though.
replyEqual area projections don't preserve distance.
replyWhat's the task here?
replyCasually looking at a map to understand relatively how far away things are from each other
replyUnless your eye can casually assemble great circle routes it's hopeless on any projection except the radial one (and then only for routes emanating from one spot)
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